Senator Elizabeth Warren (D-MA) during a Senate Banking Committee hearing. Leaders of the centrist Democrat think tank Third Way, warn that liberal Warren would be “disastrous” for Democrats heading into the 2016 presidential race.

Washington — Bill de Blasio hasn’t even been sworn in yet as mayor of New York, but he’s already a poster-child for liberalism run amok. Watch out, New Yorkers, your taxes are about to go up! “Stop and frisk” is ending, crime will rise! The city’s finances are about to collapse!

And then there’s Elizabeth Warren of Massachusetts, Mr. de Blasio’s ideological sister in the Senate, who is ready to challenge Hillary Rodham Clinton in the Democratic primary for president in 2016 – if some of the press coverage is to be believed.

Except that’s looking highly doubtful. Senator Warren has insisted repeatedly that she’s not running for president, and while that’s the standard response for anyone this early in the process, her denials make sense. She has a big megaphone in the Senate, and a big national following, less than a year into her term. And unlike Mrs. Clinton, Warren doesn’t have a shadow presidential campaign already in operation.

As for de Blasio, the demise of “stop and frisk” – the police practice of questioning and frisking suspicious-looking people, which leads to charges of profiling – may have been greatly exaggerated. In his first high-profile cabinet pick, de Blasio named former New York City Police Commissioner William Bratton to his old job. Mr. Bratton is the father of stop and frisk, though he has promised reforms.

And so, it appears, signs of a resurgent liberalism in America may too be a bit exaggerated. President Obama won kudos from the left for his Dec. 4 speech addressing the rise in income inequality, including a call for a higher federal minimum wage, but he also made a bow toward the engine of economic growth, the private sector.

“We can’t tackle inequality if the economic pie is shrinking or stagnant,” Mr. Obama said. “The fact is if you’re a progressive and you want to help the middle class and the working poor, you’ve still got to be concerned about competitiveness and productivity and business confidence that spurs private sector investment.”

By the sound of it, the president is trying to strike a balance between competing strains within his party: the newly energized progressive wing, which wants more government spending, higher wages, higher taxes, and expanded Social Security; and fiscal moderates, who still hope for a “grand bargain” with Republicans that includes entitlement reforms (read: cuts), even though the two parties have given up on the idea for now.

A flareup in this long-running competition burst forth last week with an op-ed by leaders of the centrist Democrat think tank Third Way, who wrote that the economic populism of de Blasio and Warren would be “disastrous” for Democrats heading into 2016.

Third Way’s president, Jon Cowan, and senior vice president for policy, Jim Kessler, pounded on Warren, in particular, calling her the leader of a movement that “relies on a potent ‘we can have it all’ fantasy” of higher taxes on the wealthy, closing corporate tax loopholes, and breaking up big banks.

If that were to happen, the fantasy continues, “then – presto! – we can pay for, and even expand, existing entitlements,” they write. “Meanwhile, we can invest more deeply in K-12 education, infrastructure, health research, clean energy, and more.”

Warren responded by calling on major financial institutions to disclose their donations to think tanks. (It’s no secret that Third Way benefits from Wall Street money.) Members of Congress who serve as honorary co-chairs of Third Way condemned the op-ed. Progressive groups gathered 125,000 signatures on a petition objecting to the piece, and delivered them to Third Way.

But in the real world of congressional budget-making, something remarkable happened: On Tuesday, the Democratic and Republican chairs of the two congressional budget committees reached a compromise. The deal pared back automatic spending cuts in both defense and domestic spending, but skipped a provision dear to the left – an extension of unemployment benefits for 1.3 million long-term unemployed Americans. Democrats grumbled, but most went along.

The bill passed the House with a large, bipartisan majority. But by Friday, it faced trouble in the Senate – and it’s Republicans who are balking. Some are tea party types, some are likely running for president, others are up for reelection and face tea party primary challengers.

So for now, it appears, the political universe is back to where it’s been since Obama was elected: the Democrats largely united when it counts, and Republicans fractured.

Al From, the founder of the old centrist Democratic Leadership Council (DLC), looks at the latest skirmish between progressive and moderate Democrats, and shrugs.

“I guess I think it’s not as much as it might appear,” says Mr. From, who has just written a book called “The New Democrats and the Return to Power." It is a history of the DLC and how - as he sees it - Bill Clinton and New Democrat principles saved the Democratic Party from the political wilderness.

Going forward, From says, questions about Obama’s political posture – Is he taking a left turn in his second term or not? – are less important than the Democrats’ need to prove that they can govern. Given the profound problems in implementing health-care reform, the jury is out.

“Liberals like to talk rhetorically about all these great goals that most of us share,” From says. “But for Democrats, it’s absolutely essential that government works, and that people don’t lose faith in government. That’s been a cornerstone principle.”